Section 4 3 TRƯỜNG ĐIỆN TỪ

Slide Presentations for ECE 329,
Introduction to Electromagnetic Fields,
to supplement “Elements of Engineering
Electromagnetics, Sixth Edition”
by

Nannapaneni Narayana Rao

Edward C. Jordan Professor of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
Distinguished Amrita Professor of Engineering
Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India


4.3
Magnetic Materials


4.3-3

Magnetic Materials
are based upon the property of magnetization, which is the
phenomenon of creation of magnetic dipoles within the
material.

Diamagnetism:
A net dipole moment is induced by changing the angular
velocities of the electronic orbits.

I

+

A

e
I

Dipole moment
m = IA an


4.3-4

Paramagnetism
Already existing dipoles are acted upon by a torque.

I dl × B
I
B
I dl × B

I


4.3-5

The phenomenon of magnetization results in a magnetization
current in the material which produces a secondary B.
 J S 0a y
z=d

Ba

m  m 0
z=0
J S 0a y

z=d

J mS  J mS 0a y

Bs
z=0

J mS  J mS 0a y

Bt


Magnetization Current

4.3-6


4.3-7

To take into account the effect of magnetization, we define the
magnetic field intensity vector, H, as
H

B
 M
0

m B
B


 0 1  m  0
B

 01  m 
B

 0 r
B
 A m


  permeability, H m
r  relative permeability

r and  vary with the material, implicitly taking into account
the effect of magnetization.


4.3-8

As an example, consider

 J S 0a y
z

m

y

x

J S 0a y

Then inside the material,



B = J S 0a y × az   J S 0a y  × az 
2
2
  J S 0 ax
B
H   J S 0 ax



4.3-9

D4.6

 0.1 a y
z=d

z

 100  0
z=0
0.1 a y

For 0 < z < d,
(a) H  0.1 a y × a z  0.1 a x A m

y

x


4.3-10

(b) B =  H = 100  00.1 a x 

10  0ax Wb m2
 4 10 6 ax Wb m2
(c) M 

B
 H
0

= 10 ax  0.1 ax
 9.9 ax A m